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Roll-on and roll-off (Ro-Ro) ships are economical transportation vessels that are very useful for transporting large freights, such as plant equipment and aircraft bodies. To load a large freight on a Ro-Ro ship, a tractor is generally used to pull a trailer on which the cargo is secured via a ramp from the port berth to the ship deck. In the case of a long cargo, the trajectory of the trailer is not the same as that of the tractor, which can cause a collision with the ramp or the gate or obstacles on the deck. Also, if the freight is too high, it may overturn when the trailer is tilted due to the ramp slope. This research proposes a method for calculating the best and safest trajectories for large freights to be loaded on Ro-Ro ships without the occurrence of any collisions or overturns. By reasonably assuming a low speed of the tractor, the proposed method generates all the possible tractor paths based on the Bezier curve and also calculates the trajectories of trailers when moving on inclined ramps; thus, it is the first method to calculate 3D trajectories for trailers when the tractor and trailer move on different planes. Besides, it searches for the best paths without any collisions or overturns and with the minimum shipping time possible. Since the proposed method calculates the paths by taking the ramp angle as a variable input, the trajectories can be automatically generated based on the change in the waterline of the ship according to the loading of the cargoes. Overall, the proposed method can be useful for transportation companies when planning the shipping of large freights, and it can also be beneficial for future autonomous driving systems.

Automatic path generation for tractor-trailers according to the ramp slope of Ro-Ro ships